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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 43e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 43e

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# Linear approximation Write an equation of the line that

ISBN: 9780321570567 2

## Solution for problem 43E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 43E

Linear approximation ?Write an equation of the line that represents the linear approximation To the following functions at a. Then? (?a)? ?graph the function and the linear approximation near a:? (?b?) ?use the linear approximation to estimate the given quantity; and? (?c?) ?compute the percent error in your approximation. f?? ?)=?ex; a? = 0? 0.03

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Solution 43E STEP 1 .The linear approximation formula is given by y = L(x) = f(a)+f (a)(xa) x Given f(x) = e and a = 0. 0 f(a) = e = 1 Then f (x) = ex f(a) = e = 1 Therefore y = L(x) = 1+1(x0) = 1+x Thus we get L(x) = 1+x Thus we get the equation of the line as y = (1+x) STEP 2 (a).graph the function and the linear approximation near a: STEP 3 (b). use the linear approximation to estimate the given quantity; 0.03 We have to estimate the value of e using the linear approximation Thus we have e0.03 L(0.03) = 10.03 = 0.97 Thus e 0.03 0.97 STEP 4 (c) .compute the percent error in your approximation. The exact value of e 0.03= 0.9704 Therefore percent error = 100× |approxexac= 100× |0.970.0.970= 100×0.00041 =0.041% |exact| |0.9704| percent error =0.041%

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 43E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 43E from 4.5 chapter was answered, more than 365 students have viewed the full step-by-step answer. The answer to “Linear approximation ?Write an equation of the line that represents the linear approximation To the following functions at a. Then? (?a)? ?graph the function and the linear approximation near a:? (?b?) ?use the linear approximation to estimate the given quantity; and? (?c?) ?compute the percent error in your approximation. f?? ?)=?ex; a? = 0? 0.03” is broken down into a number of easy to follow steps, and 55 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Approximation, Linear, graph, Error, estimate. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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